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Implementation of New TPD Analysis Techniques in the Evaluation of Second Order Desorption Kinetics of Cyanogen from Cu(001) Erkan Z. Ciftlikli,† Everett Y. M. Lee,† James Lallo,† Sylvie Rangan,‡ Sanjaya D. Senanayake,§ and B. J. Hinch*,† †
Department of Chemistry and Chemical Biology, Rutgers, the State University of New Jersey, 610 Taylor Road, Piscataway, New Jersey 08854, United States, ‡Department of Physics and Astronomy, Rutgers, the State University of New Jersey, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, United States, and § Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973, United States Received June 7, 2010. Revised Manuscript Received September 30, 2010
The interactions of cyanide species with a copper (001) surface were studied with temperature programmed desorption (TPD) and X-ray photoelectron spectroscopy (XPS). Adsorbed cyanide species (CN(a)) undergo recombinative desorption evolving molecular cyanogen (C2N2). As the adsorbed CN species charge upon adsorption, mutually repulsive dipolar interactions lead to a marked desorption energy reduction with increasing CN(a) coverages. Two new TPD analysis approaches were developed, which used only accurately discernible observables and which do not assume constant desorption energies, Ed, and pre-exponential values, ν. These two approaches demonstrated a linear variation of Ed with instantaneous coverage. The first approach involved an analysis of the variations of desorption peak asymmetry with initial CN coverages. The second quantitative approach utilized only temperatures and intensities of TPD peaks, together with deduced surface coverages at the peak maxima, also as a function of initial surface coverages. Parameters derived from the latter approach were utilized as initial inputs for a comprehensive curve fit analysis technique. Excellent fits for all experimental desorption curves were produced in simulations. The curve fit analysis confirms that the activation energy of desorption of 170-180 kJ/mol at low coverage decreases by up to 14-15 kJ/mol at CN saturation.
1. Introduction Cyanide is a potent ligand and pseudohalogen with a strong affinity for forming ionic compounds or complexes with many transition metals. Cyanides have a number of uses in a large number of industries, notably in mining and electroplating.1 Also, as cyanide is isoelectronic with NOþ and CO, it is often used in comparative studies. There has therefore been much interest in the properties of cyanide-surface binding on metallic faces.2,3 Cyanogen, C2N2, often undergoes dissociative adsorption on metallic faces. The electrophilic adsorbed cyanide radical (CN) readily picks up charge from the surface. The transfer of charge, from surface to isolated CN species, is believed to be up to the order of 0.7e-/CN on single crystal surfaces.4 The resultant cyanide anion therefore can be strongly ionically chemisorbed. An advantage of cyanogen as the means of CN deposition is that only the CN species is deposited. In contrast, for example, with HCN exposures, the codeposition of H can potentially lead to other coadsorbed species.5,6 In this study, we focus on the high surface temperature desorption of neutral cyanogen from copper (001) to investigate not only CN/surface binding but also to characterize mutual CN(a)-CN(a) *To whom correspondence should be addressed. E-mail: jhinch@rutchem. rutgers.edu. Telephone: 732-445-0663. (1) Guzman, L.; Segarra, M.; Chimenos, J. M.; Cabot, P. L.; Espiell, F. Electrochim. Acta 1999, 44(15), 2625–2632. (2) Harrison, M. J.; Woodruff, D. P.; Robinson, J. Surf. Sci. 2006, 600(2), 340– 347. (3) Ample, F.; Curulla, D.; Fuster, F.; Clotet, A.; Ricart, J. M. Surf. Sci. 2002, 497(1-3), 139–154. (4) Bauschlicher, C. W., Jr. Surf. Sci. 1985, 154(1), 70–78. (5) Jentz, D.; Mills, P.; Celio, H.; Trenary, M. Surf. Sci. 1996, 368(1-3), 354– 360. (6) Celio, H.; Mills, P.; Jentz, D.; Pae, Y. I.; Trenary, M. Langmuir 1998, 14(6), 1379–1383.
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interactions. Through a simple chemical consideration, a CN adsorbate on a conducting surface will pick up a net negative charge. However, on the metallic face, a marked screening of the ionically bound adsorbate, as is observed in density functional theory (DFT) Generalized Gradient Approximation (GGA) calculations,7 also leads to a dipole localized at each adsorbate. The mutually repulsive interaction of surface dipoles is, of course, coverage dependent; that is, the binding energy of any one ionically bound moiety should decrease with increasing coverage. While the activation energy of desorption increases with decreasing surface coverage, the exact dependence of activation energies on surface coverage is not easily predicted. Surface mobilities, the relative binding and interaction energies, as well as the extent of depolarization at higher coverages all play roles in determining the exact coverage dependence of thermal desorption energies. This adsorption system, however, is one in which one would predict a moderate to strong coverage dependence of thermal desorption energies which has been used to test the new temperature programmed desorption (TPD) analysis techniques introduced here. TPD is a commonly used technique in evaluating the kinetics of gas evolving surface reactions.8-13 TPD spectra are taken during a thermal ramp of the surface temperature. Results from TPD are then usually interpreted in terms of a modified Polanyi-Wigner (7) Jacob, T. Unpublished Results. (8) De Jong, A. M.; Niemantsverdriet, J. W. Surf. Sci. 1990, 233(3), 355– 365. (9) Nieskens, D. L. S.; Van Bavel, A. P.; Niemantsverdriet, J. W. Surf. Sci. 2003, 546(2-3), 159–169. (10) Habenschaden, E.; K€uppers, J. Surf. Sci. 1984, 138(1), L147–L150. (11) King, D. A. Surf. Sci. 1975, 47(1), 384–402. (12) Masel, R. I. Principles of Adsorption and Reaction on Solid Surfaces; John Wiley and Sons. Inc: New York, 1996; p 507. (13) Redhead, P. A. Vacuum 1962, 12(4), 203–211.
Published on Web 11/19/2010
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equation: IðTÞ ¼ -
dθ 1 dθ vθn - Ed ¼ ¼ exp dT β dt β RT
ð1Þ
The scaled desorption rate, I, can be defined in terms of the instantaneous surface temperature, T, and the fractional adsorbate coverage (normalized to that of saturation coverage), θ. ν is the pre-exponential factor of desorption, n is the order of desorption, Ed is the activation energy of desorption, β is the temperature ramp rate (in K s-1), and R is the gas constant. For a perfectly linear temperature ramp only, β 6¼ β(T) and I(T) is simply proportional to the instantaneous desorption rate. Given the use of the normalized coverage, θ, 0 < θ e 1, I is expressed in units of inverse temperature (K-1), or strictly in fractional coverage per unit temperature, and ν in inverse time (s-1). In this CN/Cu(001) surface adsorbate system, the saturation coverage has been determined with X-ray photoelectron spectroscopy to be 0.41 ML.14 It is often assumed, although often unwisely, that ν, n, and Ed are close to coverage (or fractional coverage) independent. However, the coverage dependent nature of these parameters has been frequently illustrated and elucidated for surface systems with considerable adsorbate-adsorbate interactions.11,15-19 From TPD curve shapes for C2N2 from Cu(001), we shall show that Ed, as is anticipated, is not independent of coverage. Here we have taken a fixed reaction order n = 2, and ν and Ed are to be evaluated. We have also assumed that all the coverage dependence is found within Ed and that ν is effectively coverage independent. In this second order process and with application of the determined parameters, the achieved accuracy of simulated TPD curves for all investigated initial exposures suggest that the n = 2 assumption is valid over the full coverage range, and that the coverage dependence of ν is minimal. The effects of coverage variation is instead seen most notably in the activation energy of desorption, Ed(θ). Note that, for nearly ideal first order desorption processes, the testing of the constant ν hypothesis frequently requires experiments which are performed over a wide range of thermal ramp rates. In contrast, for essentially second order desorption processes, identical coverages can be achieved with differing initial exposure, that is in differing θ0, runs. Hence, in this case, varying ramp rate experiments are not necessary in indicating the negligible, and weak, coverage dependence of the pre-exponential, ν. After an experimental section, the remainder of this paper is divided into four parts. The first part reviews X-ray photoemission data from surfaces prepared by cyanogen exposures of Cu(001) at differing surface temperatures. The thermal stabilities of C2N2(a) and CN(a) are investigated. The second section briefly reviews results achieved with various conventional analysis methods for interpretation of TPD data according to the Polanyi-Wigner equation. Comparative evaluations of major TPD analysis techniques can be found also, for example, in articles published by the groups of Niemantsverdriet8,9 and Yates.20 In practice, the large (14) Ciftlikli, E. Z.; Lallo, J.; Rangan, S.; Lee, E. Y. M.; Senanayake, S. D.; Mullins, D.; Hinch, B. J. Results to be published. (15) Menzel, D. In Interactions on metal surfaces; Gomer, R., Ed.; Springer-Verlag: New York-Heidelberg-Berlin, 1975; p 101. (16) Christman, K. Introduction to Surface Physical Chemistry; Steinkopff: Darmstadt; Springer: New York, 1991, p 152. (17) Kreuzer, H. J. Z. Phys. Chem. 2009, 223(1), 105–129. (18) Menzel, D. In Chemistry and Physics of Solid Surfaces IV; Vanselow, R., Tong, S. Y., Eds.; Springer-Verlag: Berlin-New York, 1982; p 389. (19) Yates, J. T., Jr. In Thermal Desorption of Adsorbed Species; Park, R. L., Lagally, M. G., Eds.; Academic Press, Inc.: London, 1985; Vol. 22, p 425. (20) Miller, J. B.; Siddiqui, H. R.; Gates, S. M.; Russell, J. N., Jr.; Yates, J. T., Jr.; Tully, J. C.; Cardillo, M. J. J. Chem. Phys. 1987, 87(11), 6725–6732.
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majority of comparative studies have focused on first order (unimolecular) desorption with far fewer looking at the kinetics of bimolecular processes leading to desorption.21 This paper focuses on a near second order desorption process, for which we demonstrate and discuss briefly the inaccuracy of results obtainable from our data with four well-known analysis techniques (Redhead’s peak maximum method,13 “Arrhenius” plots,8 complete/ constant coverage analysis,11 and Habenschaden’s and K€uppers’ leading edge analysis8-10). In the third part, we illustrate that desorption peak shapes for a second order desorption mechanism are clearly sensitive to the variation of Ed with instantaneous coverage. In a new approach, we show how the increasing initial CN coverage dependence of TPD peak asymmetry indicates that the C2N2 desorption activation energies vary linearly with coverage. Independently we also show that Tm, θm, and Im for desorption curves, with varying θ0, allow not only qualitative but also moderately accurate quantitative determination of E°d and its coverage dependence. Finally, the fourth section uses the deduced functional form for Ed(θ) in application of a systematic curve fit analysis, in this case in the study of the coveragedependent second order process of C2N2 desorption from Cu(001).
2. Experimental Details Synchrotron X-ray photoelectron spectroscopy (XPS) was performed at the Brookhaven National Laboratory NSLS facility on the beamline U12A, equipped with a 125 mm hemispherical Omicron VSW EAC2000 electron analyzer. A copper (001) crystal was cleaned under ultrahigh vacuum (UHV) conditions with ion sputtering (with 1 keV argon ions) and sample annealing (at 673 K) cycles. The Cu sample was then exposed to a cyanogen flux using a directional doser. Absolute exposure levels are unknown, although relative exposures can be accurately determined. A monochromatic photon beam energy of ∼600 eV was used for both survey scans and more detailed scans of the C 1s and N 1s photoemission peak regions. The energy resolution is ∼0.2-0.3 eV, using a fixed analyzer transmission (FAT) mode with a pass energy of 10 eV and 100 100 slits. All cited binding energies here are referenced to Cu 3p 1/2 and Cu 3p 3/2 binding energies of bulk copper at 78.0 and 75.2 eV, respectively. Temperature program desorption experiments were performed in a UHV system, located at Rutgers, with a differentially pumped UTI quadrupole mass spectrometer at a background pressure of ∼3 10-10 mbar. The crystal was mounted on lN2-cooled tungsten supports which are used for resistive heating. A type K thermocouple was placed within a hole in the crystal side. Absolute temperatures are considered accurate to within 5 K, although temperatures are more reproducible. Dosing was achieved by backfilling the chamber with the same “99%” cyanogen (C2N2) (Linde Gas) gas source as used for the NSLS experiments. The mass spectra exhibited no observable contaminant levels in the C2N2 feed with mass spectrometry. Surface coverages were estimated from integrated peak areas of subsequent TPD spectra, normalized to that evolved from a 0.41 ML C2N2 saturated surface. The instantaneous surface coverages were also estimated from remaining integrated peak areas in any particular TPD run. Lastly, the TPD runs shown in this paper could not be allowed to run until desorption was complete, to avoid the possibility of approaching the substrate melting temperature. Runs did not exceed 890 K. Even at 3 K s-1, the desorption runs were incomplete. In practice, the final TPD sections were estimated using best fitted TPD fit parameters, in order to determine most accurately the initial CN surface coverages. After determination of each initial coverage, the generated segment of a TPD curve is thereafter disregarded. A circular use of coverage (21) Fernandez-Ramos, A.; Miller, J. A.; Klippenstein, S. J.; Truhlar, D. G. Chem. Rev. 2006, 106(11), 4518–4584.
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Figure 1. XPS scans of saturation exposures of cyanogen for (a) C 1s and (b) N 1s spectral features. The red curves indicate the results of exposures and measurements made at 173 K, whereas the black curves, indicating narrower peaks, are for exposures and measurements at 263 K. XPS scans at 263 K of (c) C 1s and (d) N 1s following 263 K saturation and 5 min anneals up to temperatures of 573, 623, and 673 K, with each showing successively smaller surface concentrations. estimates, Ed evaluation, and repeated coverage estimation showed excellent consistency. Absolute coverage estimates are considered to be accurate to within less than ∼0.02 ML. Lastly, the sample temperature ramps were not exactly linear at the extremes of the thermal ramp regions. Possible effects of nonlinearity in temperature ramps are discussed below.
3. Results and Discussion 3.1. Thermal Stability of Adsorbed Cyanide Probed with XPS. XPS was first used to characterize adsorbed species after C2N2 exposures at 173 and 263 K on the Cu(001) surface. The corresponding C 1s and N 1s XPS spectra are shown in Figure 1a and b, respectively, in black for adsorption and measurement substrate temperatures of 263 K and in red for temperatures of 173 K. For exposures at 173 K, the N 1s region shows a multicomponent spectrum, which can be decomposed into two peaks centered at 398.8 and 400.6 eV. Likewise, the C 1s XPS spectrum for this temperature comprises at least two peaks centered at 285.9 and 287.6 eV. In contrast, cyanogen deposition at 263 K leads to the appearance of the low binding energy peaks alone, in both the C 1s and N 1s regions; that is, single C 1s (at 285.1 eV) and N 1s (at 398.8 eV) peaks are observed in Figure 1a and b, respectively. The results suggest that for cyanogen deposited at 173 K more than one species is present on the surface. For the same exposure, the 173 K scans show a 55% increase in both total C and N levels over those for the 263 K exposures, in Figure 1a and b. A molecular cyanogen species in multilayer adsorption is anticipated. At 263 K deposition, the spectra are attributable to essentially only one adsorbed CN species. This dissociative behavior is analogous to that of halogens where a diatomic molecule cracks on the surface at room temperature to form only the anionic species.22,23 XPS was also used to investigate the surface after complete and partial desorption of C2N2. Between 263 and 473 K, no changes are observed in the C 1s or N 1s regions. Incomplete desorption is observed following 5 min temperature anneals to 573 and 623 K, as displayed in Figure 1c and d. In these annealing cycles, the C (22) Stott, Z. T.; Hughes, H. P. Surf. Sci. 1983, 126(1-3), 455–462. (23) Stott, Z. T.; Hughes, H. P. Vacuum 1981, 31(10-12), 487–490.
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Figure 2. Raw TPD experimental data for cyanogen desorption with varying initial cyanogen coverages. The m/z = 52 peak is monitored as representative of the desorbing molecular C2N2..
and N losses are in proportion to the original (presumably 1:1) levels, consistent with solely C2N2 desorption. After annealing to 673 K, virtually complete desorption is indicated, and there is little sign of any other residual component such as might be anticipated with C(a) or N(a) species. The latter (spectrum not shown here) exhibits a 397.2 eV feature. The cyanogen exposures, prior to all TPD experiments, were performed at room temperature. The XPS results above therefore imply that molecular cyanogen is not on the surface at the outset of temperature ramps. Complete dissociation on adsorption is fully supported. The observed molecular desorbing species is therefore formed at temperatures above RT. Our belief is that molecular association is rate determining in the TPD scans of Figure 2. Molecular desorption is facile; it occurs readily between 163 and 263 K. Figure 2 also indicates that decreasing levels of initial CN coverage, θ0, result in corresponding shifts to higher desorption temperatures. This behavior is anticipated for second order desorption kinetics in associative desorption. Hereafter, the following analysis methods, employed to find desorption energy and pre-exponential factor estimates, will assume that the desorption-order n of eq 1 equals 2. This comparatively simple associative desorption process is in contrast to what is seen after some halogen exposures. For example, a chlorine exposed Cu(001) surface will exhibit sublimation of bulk CuCl species at temperatures of ∼500 and 900 K.24 No such Cu containing species were seen to desorb with C2N2 exposures and the TPD runs. 3.2. Application of Established TPD Analysis Techniques. The commonly used Redhead’s peak maximum method13 derives from differentiation of the Wigner-Polanyi equation, eq 1. The technique also (in this case erroneously) assumes model (second) order behavior with a coverage independent desorption energy Ed. The fact that, at the temperature of maximum desorption, Tm, the derivative dI/dT is zero implies Ed 2νθm Ed 2Im ¼ ¼ exp β RTm θm RTm 2
ð2Þ
where θm is the instantaneous fractional coverage of the surface at Tm. A plot of ln(2θmTm2) vs 1/Tm therefore should show a slope equal to Ed/R and an intercept ln(βEd/νR). Figure 3a shows this (24) Nakakura, C. Y.; Phanse, V. M.; Altman, E. I. Surf. Sci. 1997, 370(1), L149–L157.
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coverage. In logarithmic form, eq 1 yields I vðθÞ Ed ðθÞ ln n ¼ ln θ β RT
Figure 3. (a) ln(2θmTm2) vs 1/Tm plot for seven individual TPD runs at varying initial coverages, derived with Redhead’s peak maximum method. A best fit straight line is shown in red. (b) TPD spectra (black) and corresponding simulated spectra (red and noise free) derived from (a), using 102.7 kJ/mol and 1.45 106 s-1. Simulated data sets utilize the experimental temperature ramps; that is, constant β values were not assumed.
plot for the data of Figure 2 and a fitted straight line. Using a best averaged value for β = 3.0 K s-1, values of Ed = 102.7 kJ/mol and a pre-exponential factor of 1.45 106 s-1 were deduced. The dependence of ln(2θmTm2) on 1/Tm appears to be accurately linear, belying the fact that simulated TPD spectra using the derived Ed and ν values, as illustrated in Figure 3b, fail to accurately reproduce the experimental TPD curves. Indeed any analysis method which assumes coverage independent Ed and preexponential values, ν, ought not be used for analysis of TPD curves such as ours. The results from the analyses, as shown here, generally cannot be used to simulate TPD peak shapes. In fitting such data with the Redhead model, an additional assumption, namely, that 2θm ∼ θ0, which is frequently used for second order processes, leads to even poorer TPD curve simulations (not shown here) wherein not even peak positions are reproduced. The asymmetries in the experimental desorption peaks (not seen in the Redhead derived simulations of Figure 3b) are the clearest indication of the inapplicability of Redhead method and the strongest indicator for coverage dependent activation energies for cyanogen desorption. A second conventional method, employing Arrhenius plots, also involves another strict treatment of the Polanyi-Wigner eq 1. For associative desorption with n = 2 and taking ν, β, and Ed as constants within a given TPD spectrum, an Arrhenius plot of ln(I(θ)/θ2) vs 1/T would have a gradient = -Ed/R and a slope = ln(ν/β). In our case, however, such plots appear linear only for surfaces with low initial coverages and visibly deviate from linearity as θ0 increases. The origin of the observed curvature in such plots is discussed in detail in the Supporting Information. The curvature is of course amplified for stronger coverage dependences of Ed(θ). In contrast to the two techniques mentioned above, the complete/ constant coverage analysis was developed to determine not only the magnitude but also the coverage dependence of Ed.11 Complete/constant coverage analysis again uses a strict interpretation of the Polanyi-Wigner eq 1. In this case, Ed(θ) represents the desorption energy of the surface species at a specific fractional Langmuir 2010, 26(24), 18742–18749
ð3Þ
By plotting a set of ln(Ij(θ)/θ2) vs 1/T at any one instantaneous fractional coverage θ, with Ij values taken from the jth number of TPD spectra, the resulting slope equals -Ed(θ)/R and the intercept equals ln(ν/β). In practice, this type of analysis gave highly fluctuating pre-exponentials ν, and we could not discern any systematic trend in the activation energy with increasing coverage. The constant coverage method clearly requires accurate estimates of coverage as well as superior signal-to-noise ratios than are seen in this C2N2 desorption data set. In analogy to the complete/constant coverage analysis, the leading edge analysis method10 addresses the coverage dependency of Ed. It is a basic and powerful technique to calculate the activation energy of desorption at given coverages by using the onset of desorption peaks. By differentiation of eq 3, the following Arrhenius equation is obtained: I ∂ln n E ðθÞ θ ¼ - d 1 R ∂ T
1 0 B 1 ∂νðθÞ 1 ∂Ed ðθÞ ∂θ C B∂lnðβðTÞÞC -B C þ @ 1 1 A νðθÞ ∂θ RT ∂θ ∂ ∂ T T
ð4Þ
The last term is comparatively small in magnitude, as compared to the other terms, as β is approximately constant. The central terms, in square brackets above, may be finite, but their significance become negligible if ∂θ ¼ IT 2 0 1 ∂ T
ð5Þ
This holds true if the desorption rate is low, that is, trivially when θ ∼ 0, or when I is small such as at the onset of the desorption peak, that is, at the leading edge. Then I ∂ln n E ðθÞ θ - d 1 R ∂ T
ð6Þ
The advantage of this technique is that it returns the value of Ed and it removes any error which can arise from assuming a coverage independent pre-exponential factor. However, being restricted to the onset of the desorption peak (where the desorption signal is weak) a superb signal-to-noise ratio is required. This is often not an easy criterion to meet and is obviously not met by our data. Yet application of this method (under specialized conditions as discussed further in the Supporting Information) gave more reliable information from our data set than could be discerned from other analysis methods discussed. Ed values are at 173 ( 8 kJ/mol. The derived parameters show much noise and a systematic coverage dependence is not apparent within the random variation of Ed. 3.3. Predicting the Functional Dependence of the Activation Energy for Desorption. As summarized in section 3.2, for DOI: 10.1021/la102304m
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Figure 4. TPD peak FWHM and asymmetry dependencies on initial coverage. (a) FWHM for model second order desorption, generated using Ed ∼ 170 kJmol-1 and ν ∼ 1011 s-1, and β = 3 K s-1. (b) Experimentally observed FWHM for CN on Cu(001). The peak asymmetry is defined as {HWHMlhs - HWHMrhs}. (c) Asymmetry for model second order desorption and (d) experimentally observed asymmetry values. Superposed here is a parabolic curve, Rθ02, suggesting that f(θ) varies linearly with coverage. The text discusses further how this deduction is made.
this CN/Cu(001) system, a marked coverage dependence in desorption energies has made the determination of activation energies for desorption unmanageable. With the available data set quality, we shall apply another approach, outlined in section 3.4, but using additional information that we derive here. Namely, we seek to determine the functional dependence of Ed(θ). 3.3.1. Qualitative Prediction of the Functional Form of Ed(θ) from the FWHM and the Asymmetry of the Desorption Peaks at Varying Initial Coverages. The nature of adsorbateadsorbate interactions will be qualitatively characterized by observing the initial coverage dependency of the full width at halfmaximum (FWHM) of a desorption peak. It is well-known that the FWHM of “model” first order desorption peaks do not change with increasing initial coverages, θ0, while for model second order desorption peaks relatively small yet detectable decreases in the FWHM with increasing initial coverages are apparent, as seen in Figure 4a. The addition of repulsive adsorbate-adsorbate interactions would reduce Ed(θ) with increasing coverage. Such interactions are thus manifest in a tendency to increase the FWHM as a function of initial coverage for either first or second order desorption peaks. For second order desorption kinetics, therefore, there can be competing effects on the FWHM variation with coverage. The experimental FWHM values from seven TPD spectra are shown in Figure 4b. It is apparent that the broadening effect of mutually repulsive adsorbate interactions dominates; that is, although the FWHM is initially constant for low θ0 spectra, a steady broadening of the desorption curves is manifest with θ0 ranging from 0.128 ML to saturation. A second key experimental parameter observed is the desorption peak asymmetry, which we define here as {HWHMlhs HWHMrhs} (HWHM, half width at half-maximum; lhs, left-hand side; rhs, right-hand side). “Model” second order desorption peaks, where Ed is constant throughout the desorption event, are close to symmetric; the asymmetry of the peak while finite is necessarily only a small fraction of the FWHMs. Simulated spectra show the small asymmetry does not change significantly with θ0 (as 18746 DOI: 10.1021/la102304m
illustrated in Figure 4c). In contrast, when repulsive forces between adsorbate moieties are present, as in CN/Cu(001), we have observed that the low sample temperature side (lhs) of a TPD peak is considerably steeper than at the higher Tx side (rhs). The observation that the asymmetry is strongly negative results from an increasing instantaneous Ed(θ) as Tx increases and θ simultaneously decreases. Consequently, a strong variation of asymmetry is also observed as a function of θ0, as is shown in Figure 4d. Let us take Ed(θ) = Ed° - f(θ), where Ed° = Ed(θ = 0) and f(θ) is as yet an unspecified function of the instantaneous coverage, θ. Note: the pre-exponential factor, ν of eq 1, is assumed to be independent of coverage and temperature, which is in accordance with the suggestions of Soler and Garcı´ a.25 The coverage independence of n is also assumed. The two previous paragraphs gave a brief summary of qualitative effects of repulsive adsorbate interactions on the FWHM and asymmetry of the desorption peaks. However, to determine Ed(θ) and ν by application of a curve fitting routine to the experimental data seen in Figure 2, an approximate functional form for f(θ) needs to be assessed. To address this, we have utilized a number of independent TPD simulations for a second order desorption process, employing various forms of f(θ) together with a set of predetermined Ed and ν values, to observe the relationship, if any, between f(θ) and FWHM(θ0) as well as between f(θ) and the TPD peak asymmetry(θ0). We have observed that, for any “reasonable” functional form of f(θ), the relationships 7 and 8 below hold well and provided f(θ) and df(θ)/dθ are small, that is, if f(θ) e E°/10 d df(θ)/dθ e Ed°/10. Namely, ½FWHM - FWHMmodel
2nd order R
f ðθ0 Þ
ð7Þ
and ½asymmetry - asymmetrymodel
2nd order
asymmetry R - ½f ðθ0 Þ2 ð8Þ
(25) Soler, J. M.; Garcı´ a, N. Surf. Sci. 1983, 124(2-3), 563–570.
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where, as before, the TPD peak “asymmetry” is defined as {HWHMlhs - HWHMrhs}. The above observations, verified with simulations with predetermined Ed, ν, and f(θ), suggest that the FWHM and the asymmetry of TPD spectra can be used to characterize the functional form of f(θ). In its current form, we do not apply eq 7 directly, as the magnitude of Ed° is unknown, and hence, we cannot immediately subtract the appropriate FWHMmodel_2nd_order for use with the experimental data sets. On the other hand, since the variation in asymmetrymodel_2nd_order is close to zero for the whole range of θ0, then the magnitude of the variations in the experimentally observed asymmetry can be approximated to be proportional to the square of the f(θ0). The observed “asymmetry” parameter as a function of initial coverage in Figure 4d fits well to a quadratic function of coverage, with zero gradient as θ0 approaches 0, suggesting that Ed varies approximately linearly with coverage, that is, for C2N2 desorption from the Cu(001) surface, Ed ¼ Ed° - Cθ
ð9Þ
where the proportionality constant C is yet to be determined. 3.3.2. Quantitative Determination of f(θ) from Experimentally Determined Parameters, Tm, θm, and Im. Our second method for predicting the functional form of f(θ) involves the monitoring of Tm, θm, and Im for TPD peaks associated with varying θ0. Since Ed(θ) = Ed° - f(θ), the Polanyi-Wigner equation becomes ! ðEd° - f ðθÞÞ νθ2 exp ð10Þ IðTÞ ¼ β RT Differentiating both sides of the eq 10 with respect to T, E ° - f ðθÞ dI νθ ¼ exp - d RT dT β
! - 2I þ
θ RT 2
! df ðθÞ T - f ðθÞ þ Ed° dT
ð11Þ Using df(θ)/dT = [df(θ)/dθ][dθ/dT] and that at the desorption peak maximum, the differential in eq 11 equates to zero, dI/dT = 0, at T = Tm, I = Im, and θ = θm. This leads to df ðθÞ 2Im RTm 2 ° ð12Þ Ed - f ðθm Þ I m Tm ¼ dθ θm θm
There are three obvious observations about eq 12. Foremost, the equation reduces to eq 2 in the absence of f(θ). Second, the right-hand side of eq 12 is evaluable from values that can be extracted easily from desorption curves. Third, the magnitudes of both the second and third terms of the left-hand side of eq 12 approach zero in the limit of zero initial coverage, that is 2Im RTm 2 ° ð13Þ Ed ¼ θm θm f 0
Another important property of eq 12 is that the magnitude of the third term of the left-hand side of eq 12 is several times larger than that of the second term, that is, for positive f(θ), 0 1 df ðθÞ A @ ð14Þ Im Tm . f ðθm Þ dθ θm
This was borne out by a number of independent simulations with various predetermined Ed° and f(θ) combinations, and is perhaps Langmuir 2010, 26(24), 18742–18749
not surprising if one looks at the approximately equivalent inequality 0 1 df ðθÞ FWHM A θ0 @ . ð15Þ dθ Tm f ðθm Þ θm
which is derived from eq 14 by using only FWHM Im ∼ θ0. If f(θ) takes a form of ∼ θp where the exponent p > 0, the lhs of eq 15 ≈ p/2. As we invariably see Tm . FWHM for almost any peak derived from activated desorption, eq 15 holds true and hence also eq 14, provided that [d ln f(θ)/d ln θ]|θm J 1, that is, if p ,e 1. Thus, incorporating eqs 13 and 14 into eq 12: 0 1 1 ! 0 2 2 df ðθÞ 2I RT 2I RT m m m m A -@ -@ AI m T m Δ ¼ dθ θm θm θm
θm f 0
ð16Þ Note that the right-hand side of eq 16 can still be evaluated experimentally; however, determination of its second term, which equals E°, d is made via an extrapolation. Thus, accuracy of the result obtained depends on the number of TPD measurements with low initial coverages as well as the reliability of their Tm, θm, and Im values for each low θ0 desorption curve. Finally, rearranging eq 16: 0 1 df ðθÞ Δðθm Þ A @ ð17Þ dθ I m Tm θm
Equation 17 suggests that we can determine the approximate functional form of the differential of f(θ) with respect to θ by using the experimental desorption curves. The differential can then be used to determine the functional form and magnitudes of f(θ) for θ below or equal to the highest observed θm. The Redhead approach used earlier utilizes Tm, θm, and β to find Ed and ν. In the approach described here, we utilize Tm, θm, β, and Im for each θ0 desorption curve. Just as discussed earlier, it is unwise to approximate θ0 ∼ 2θm especially for the higher θ0 desorption curves. In either of the approaches, θm needs to be estimated from the desorption curves. Consequently, only one additional (easily approximated) value from each desorption curve is needed for the later analysis method, namely, Im. The results of applying this methodology to our TPD spectra are outlined in Figure 5. Figure 5a indicates experimentally extracted values of the right-hand side of the eq 12. A simple visual extrapolation of the seven point curve in Figure 5a to θm = 0 suggests that E°d takes a value of approximately 180 kJ mol-1. Placing this value into eq 16 returns the values of Δ. We can thus evaluate the right-hand side of eq 17. The results, shown in Figure 5b for the seven desorption spectra, indicate that the differential of f(θ) with respect to coverage is essentially coverage independent and floats in the 14-17 kJmol-1 range. This result clearly implies that f(θ) is linearly dependent with θ in the given coverage range. The proportionality constant C is ∼15 kJ mol-1. This outcome was fully supported by the qualitative conclusion reached in section 3.3.1. This adsorption system was predicted and verified to have a measurable coverage dependence of the thermal desorption energies. The apparent linear dependence of Ed on θ is unanticipated but can most easily be explained in terms of coverage independent normalized pairwise-correlation functions for CN species, and of screened (coverage independent) dipole moments. At the temperatures near to those required for C2N2 desorption CN species DOI: 10.1021/la102304m
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Figure 5. (a) Values of the right-hand side of eq 12 determined from the seven TPD curves presented in Figure 2. Extrapolation of these values to zero peak maximum coverage is predicted to yield Ed°. (b) Values of Ed°/ImTm - 2RTm/θm as indicated by eq 17 for the same TPD curves.
are presumed to be mobile, and thermal energies can exceed all but nearest neighbor interaction energies. On this basis a mean field approach to long-range dipolar interactions seems warranted. Provided that neither the distance of closest approach between two CN species, nor the dipole moment of any adsorbed CN species, are strongly coverage dependent then the destabilization of any one CN species due to electrostatic interactions will be simply proportional to the overall CN coverage. Thus any pair of potentially reactive CN species has, at its ground state, an energy that is modified also in proportion to the coverage. Consequently a linear dependence of Ed on θ can be rationalized. In practice none of the approximations suggested here need to be accurately adhered to, but deviations might still be able to work toward the same final result, a coverage independent C parameter. 3.4. Curve Fitting Method. Utilizing the simple linear functional form for f(θ), it is now possible to fit most accurately each TPD curve with one kinetic model for desorption. In doing so, we use all data in a given TPD curve. Explicitly, we have run an optimization routine, implemented in Maple 11, for minimization of mean square differences between observed data and simulated desorption runs within the following model: " # - ðEd° - CθÞ vθ2 ð18Þ exp IðTÞ ¼ RT β The actual temperature ramp rate β, monitored during data acquisition, is used both in displaying -dθ/dT shown in the experimental TPD spectra and in simulating this data. The assumption of a constant β can lead to considerable inaccuracies in many cases. In our fitting routine, ν, E°, d and C are the only free parameters while others are experimentally determined. As is well-known, these parameters can be closely coupled:20 for example, changes in either Ed or ν can be nearly compensated with variation of the other. A simple fitting procedure of a TPD run can therefore easily return an inaccurate combination of (ν, Ed°, C). In practice, we have found it just as easy to do a systematic search through all parameter space, rather than applying a method of steepest descent. Therefore, we first sample three-dimensional (ν, E°, d C) space, in small sized steps, and compare the simulated data sets 18748 DOI: 10.1021/la102304m
Table 1. Best Fit Combinations of (ν, Ed°, C) for Individual TPD Runs with Indicated θ0 Values initial coverage
Ed° (kJ/mol)
ν (s-1)
C (kJ/mol)
0.41 ML 0.386 ML 0.325 ML 0.302 ML 0.189 ML 0.129 ML
177 174 178 176 171 173
1.02 1011 6.2 1010 9.4 1010 6.3 1010 4.7 1010 5.1 1010
14.4 13.8 15.2 14.3 15.2 15.5
with the experimental TPD scan, taken at any of the six different initial coverage levels ranging from 0.128 to 0.41 ML. We chose not to utilize the TPD curve with the lowest θ0 only, as the signalto-noise ratio was considered poorer. Then, in a second step, we perform the curve fit searches in the proximity of a number of “good” (ν, E°, d C) combinations, which were found through our initial wider 3-D surveys. Thereby, we are confident in having finally found the (ν, Ed°, C) combinations corresponding to the global minima in square error sums. The best fit combinations of (ν, E°, d C) for individual TPD runs are listed in Table 1. The results indicate an ∼5% uncertainty in zero-coverage activation energy of desorption (Ed°) for the six desorption curves utilized. The variation in ν just exceeds a factor of 2. (An order of magnitude uncertainty in ν is equivalent to ∼7.5% uncertainty in Ed.25) The spread in C is ∼1.4 kJ/mol which is less than 1% of Ed only. A visual comparison all seven TPD spectra and the corresponding simulations, performed by employing only an average of the fitting results, that is, E°d = 175 kJ/mol, ν = 7.0 1010 s-1, and C = 14.7 kJ/mol alone, is shown in Figure 6. As the fits to the TPD spectra, using this single (ν, Ed°, C) set, are satisfactory for all initial coverages ranging from 0.074 ML to saturation 0.41 ML, the assumed linear relation between the activation energy of desorption and coverage is validated. It should be noted that the deduced magnitude of ν for C2N2 desorption is significantly smaller than 1013 s-1, and is smaller than other tabulated ν values for various second order desorption processes presented elsewhere.15,26 This fact must be interpreted in terms of coverage independent entropy differences between an (26) Wang, Z.; Seebauer, E. G. Appl. Surf. Sci. 2001, 181(1-2), 111–120.
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Figure 6. Simulations (smooth red curves) and experimental TPD spectra (noisier black curves). The simulations employed one set of Ed° = 175 kJ/mol, ν = 7.0 1010 s-1, and C = 14.7 kJ/mol for all seven TPD data sets displayed. The initial coverages of simulated CN/Cu(001) surfaces are ranging from 0.074 to 0.41 ML.
initially dissociated CN pair and the molecular-like C2N2 transition state. The obvious configurational entropy difference required for independent alignment of two CN species along the approach for an associative reaction must go part way to explaining the low pre-exponential factor here. In this respect, any desorption process involving association of diatomic or larger subunits might be expected to have pre-exponential values below 1013 s-1, as is found for C2N2 desorption.
4. Conclusions Part of the challenge of finding realistic values of desorption energy and pre-exponential values is in finding a reliable analysis technique. Four literature techniques (Redhead’s peak maximum method, the complete/constant coverage analysis, HabenschadenK€uppers/leading edge analysis, and “Arrhenius” plots) as well as a fifth technique based on curve fitting have been used to independently estimate the desorption energies and pre-exponential factors for the recombinative desorption of cyanide to cyanogen on a copper (001) surface. It was shown that, due to the anticipated deviation from model second order behavior, the Redhead’s peak maximum method and “Arrhenius” plots were unsuitable in determining the aforementioned parameters. In the case of the constant coverage analysis, the values obtained for desorption energy and pre-exponential were highly inaccurate and erratic due to this technique’s high sensitivity to errors in coverage estimation and its requirement of superb signal-tonoise quality in the spectra. While a modified HabenschadenK€uppers/leading edge approach analysis suggested a desorption energy in the range of 165-181 kJ/mol under the most reliable conditions, the technique, however, could not provide systematic results for the coverage dependence of the desorption energy. Only the fifth technique, that is, a determination of the functional form of the coverage dependence of Ed followed by the curve fit analysis, provided consistent values of desorption energy in the limit of zero coverage (171-178 kJ/mol) and a pre-exponential (∼7 1010 s-1) for all the initial CN coverages studied, and this was only obtained when a linear mutual-repulsion factor C (= ∼14.7 kJ/mol) was introduced into the Polanyi-Wigner equation. In moving from the lowest to the highest CN coverages (0.41 ML), the activation energy for desorption was shown to decrease by approximately 8%, namely, from 175 to 160 kJmol-1. This fractional variation in Ed we have found is sufficient that neither Langmuir 2010, 26(24), 18742–18749
the Redhead nor Arrhenius analysis methods could be reliably applied to this desorption system. Application of the curve fit analysis was possible essentially only after the determination of the functional form of the coverage dependency of Ed. Two different approaches were introduced here to achieve this prerequisite, both suggesting that the CN coverage dependence of Ed was accurately described by a linear form. First the peak asymmetry, while not exactly zero for ideal second order desorption process, exhibits a variation that appears proportional to the square of the initial coverage. Second, a novel quantitative technique based upon monitoring Tm, θm, and Im values of TPD spectra with changing θ0 is in full agreement with the last result. The latter technique is simple, quantitative, and powerful, but it has limitations. (a) Equation 17 is useful within a limited coverage range 0 < θ e θsat m . In other words, we are not able to see whether the functional form of f(θ) differs for coverages that exceed θsat m, sat that is, in the range of θsat m < θ e θ . (b) Although the technique returns the value of Ed° directly and f(θ) by integration of the righthand side of eq 17, the accuracy of the results, especially in determination of E°, d depends on the quality of the data, that is, on the precision of the experimentally obtained parameters, Tm, θm, and Im. Despite these limitations, (a) and (b), the accuracy far exceeds that achieved with the four tested methods using our data set (without the best of TPD signal-to-noise ratios). Lastly, f(θ) = Cθ does appear to hold also for θ > 0.5, that is, for coverages in excess of 0.2 ML up to ∼0.41 ML, as the simulated curves of Figure 6 fit the data well even for the leading edges of the highest initial coverage TPD curves. Briefly, Redhead’s analysis method has been widely applied, despite its limitations to systems that show only very weak coverage dependent activation energies, essentially because the analysis requires only knowledge of θm (or even just θ0) and peak maxima temperatures, Tm, alone. The method is thus popular and very easy to implement even with data sets of comparatively poor signal-to-noise ratios. However, when systems are expected to show coverage dependent desorption energies, the method is typically either applied unwisely or not applied at all. We have now illustrated approaches, in sections 3.3.1 and 3.3.2, which use only one more readily attainable parameter from data sets, namely, Im. We have shown that the new means for estimating Ed(θ) are both rapid and accurate; the new approaches will be easily applicable in many other adsorption systems. Acknowledgment. The work was supported by the NSF, CHE-0718055. The U12a beamline and S.D.S. have been supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC05-00OR22725 with Oak Ridge National Laboratory. The National Synchrotron Light Source, Brookhaven National Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886. Supporting Information Available: (A) Results of the analysis using Arrhenius curves and the machinery for understanding the curvature in Arrhenius curves. Comparison between an experimentally obtained Arrhenius curve and the simulated one obtained with using f(θ) = Cθ. (B) Discussion of how more consistent results can be obtained from our data using Habenschaden’s and K€ uppers’ leading edge analysis approach as was briefly discussed in section 3.2 above. This material is available free of charge via the Internet at http://pubs.acs.org. DOI: 10.1021/la102304m
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